Probability and Statistics: The Basics

If you’re like me, the words “probability” and “statistics” probably make your eyes glaze over. This article is going to break down some of the basics in a way that won’t put you to sleep (hopefully).

Probability deals with predicting outcomes based on past data, while statistics involves analyzing and interpreting that data. Both fields are incredibly important for making informed decisions about everything from medical research to financial planning.

Let’s start with some basic terms you might encounter when talking about probability:

– Experiment: a procedure that results in well-defined outcomes (e.g., flipping a coin)
– Outcome: any possible result contained in a sample space (e.g., heads or tails for the flip of a coin)
– Sample space: all possible outcomes of an experiment form a sample space (e.g., S = {heads, tails} for the flip of a fair coin)
– Event: an event is any subset of a sample space (e.g., A is the event that a fair six-sided die lands on an even number)
– Trial: each flip of a coin or iteration of an experiment is referred to as a trial (in the example above, each flip of the coin is a trial in the experiment of flipping a coin to determine the number of heads)

Now that we’ve got those terms down, probability itself. Probability theory allows us to predict the chance of a given outcome occurring based on past data or assumptions (if you don’t have any actual data). For example, if we assume that a coin is fair (meaning it has an equal chance of landing heads up or tails up), then the probability of flipping a head is 0.5 (or 1/2) because there are two possible outcomes and one of them is what we’re looking for.

There are many different types of events in probability, but let’s focus on three: simple events, compound events, and independent events. A simple event has only one outcome (e.g., flipping a coin and getting heads), while a compound event involves multiple outcomes happening at the same time (e.g., flipping two coins and getting both of them to land on heads). Independent events are events in which the outcome of one event is unaffected by the outcome of another event (flipping a coin is an example of an independent event because each flip has an equal chance of landing heads or tails, regardless of what happened on previous flips).

Dependent events, on the other hand, are events in which the outcome of one event affects the outcome of another event. For example, if we remove a blue marble from a bag containing 3 blue marbles and 2 red marbles, then the probability of selecting a blue marble on a subsequent trial is no longer 60% (since there are now only 2 blue marbles left in the bag).

Finally, some basic rules for calculating probabilities. The addition rule allows us to find the probability of two events occurring at the same time if they are not mutually exclusive (meaning they can both happen simultaneously), while the multiplication rule is used to calculate the probability of two events happening in sequence. Bayes’ rule, which we won’t go into too much detail about here, allows us to find the probability of an event given that another event has already occurred.

If you want to learn more, I highly recommend checking out some resources online or consulting with a statistician if you’re working on a research project that involves data analysis.